Class jBJ Book_ _^„ PRESENTED BY ^-7— ■■■■■■ HH MENTAL FATIGUE DURING CONTINUOUS EXERCISE OF A SINGLE FUNCTION BY THOMAS RUSSELL GARTH Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Faculty of Philosophy, Columbia University 1918 7 / MENTAL FATIGUE Digitized by the Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/mentalfatiguedurOOgart MENTAL FATIGUE DURING CONTINUOUS EXERCISE OF A SINGLE FUNCTION BY THOMAS RUSSELL GARTH Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Faculty of Philosophy, Columbia University '^^ ^\ /V^V^^*"^ »K-*fA 1918 .G;3 m 21 isis The writer makes the following acknowledgments: To Dr. R. S. Woodworth for valuable suggestions in the handling of the data and criticism of the calculations; to Dr. E. L. Thorndike for use of his addition sheets and suggestions as to the conduct of the ex- periment; to his wife, Ethel Nadine Garth, who corrected some of the sheets and assisted in the tabulation and without whose en- couragement the enormous task of correcting the 12,355 papers and that of their tabulation and the many and various calculations might never have been brought to completion. My thanks are due also to Dr. J. A. C. Chandler, Superintendent of City Schools of Richmond, Va., and his first assistant, Mr. A. H. Hill, for access to the classes of the schools of that city; to Mr. F. M. Martin for the same courtesy in the Petersburg, Va., schools, and to the prin- cipals and teachers who rendered valuable assistance in giving the tests; and to Mr. S. P. Duke, Head of the Department of Educa- tion of the State Normal School of Farmville, Va., for much appre- ciated assistance while tests were being given in Richmond. INTRODUCTION A SURVEY OF THE SUBJECT OF MENTAL FATIGUE DURING CONTINUOUS EXERCISE OF A SINGLE FUNCTION So far the investigations of various experimenters in the field of Mental Fatigue during continuous exercise show that continuous work under the lash of keen motivation reduces the efficiency only slightly, even though the subjects worked from one to two hours. Burgerstein, 'pi, found in an experiment with a large group of boys, aged eleven to thirteen years, in which the pupils performed easy examples in addition and multiplication in ten-minute periods with five-minute rests between, that the number of examples increased as the test proceeded, but there were more errors and corrections made by the pupils as the work went on. Hopner, '94, undertaking to make the exercise more like that of the ordinary recitation, had a class of forty-six boys, of average age, nine years, write nineteen sentences from dictation. Each sentence was read aloud to the class once, then it was repeated once by a single pupil, next by the entire class, and then the pupils were re- quired to write it from memory. The experiment extended over two hours. Hopner found that as the time proceeded, the pupils became less exact. Colloquial speech often took the place of the words in the dictated sentence. It is very evident that the materials for the experiment were not of equal difficulty. Neither were the pupils pressed to their utmost. (Offner & Whipple, Mental Fatigue, 57ff.) Holmes, '95, had children from Grades Three to Eight add num- bers for thirty-six minutes and broke the time into four periods of nine minutes each. There was an increase in errors of adding and copying. But when everything in the way of length of problem and speed is taken into consideration, the decrease in efficiency is not very great. Cattell and Dolley found that simple reaction-time is not influ- enced by previous reactions to any great extent. Vlll INTRODUCTION Thorndike describes an experiment of continuous mental work "of from three to eight hours" which "failed in the case of Dr. R. S. Woodworth, to produce any demonstrable diminution in efficiency." One part of the experiment was to mark the e's and t's in a book of 151 pages. This process continued for eight hours with less than nine minutes interruption. (See Thorndike's Educational Psy- chology, Vol. Ill, pp. 29-32.) Thorndike, 'u, had fourteen students work from four to fourteen hours doing mental multiplication of three-place numbers by a like number. Six of these individuals took fifty-four per cent, more time for the end of the period on one day than they did at the beginning of the period for the preceding day. Six others had an average increase of fifty-nine per cent. For the other two, the increase was twenty-one per cent. Arai, '12, had eleven students perform multiplication of two-place numbers mentally for two hours on two occasions. The intermis- sions were not the same for all participants in the experiment. The measure of efficiency was the time required for each example. It was found that the time was reduced. In performing the multi- plications this means that there was an increase in efficiency. Kraepelin worked out a method for continuous adding. A note- book is prepared with numbers printed in vertical columns. A bell is made to ring every five minutes and when the subject hears the bell he makes a mark. In this way the record is made according to the time worked. Kraepelin and his followers (Offner & Whipple, pp. 62-73) claim to have found certain interesting features in the work curve. These are practice, warming-up (Anlauf), swing (Anregung), spurt (Antrieb), initial spurt if it occurs at the beginning and 'spurt of change' if it occurs when a new kind of work begins, and 'terminal' spurt or end spurt (Schlussantrieb) when the subject realizes that he is nearing the end of the experi- ment or exercise. Thorndike's absolutely fair treatment of the results and data of Kraepelin's work and of those who follow him brings into question the existence of such features in all work curves, and calls for further proof of their existence. He says: "Two hours or less of continu- ous exercise of a function at maximum efficiency produce a tempo- rary negative effect . ... of not over ten per cent, and in most func- tions still less than that." * 1 Educational Psychology, Vol. Ill, pp. 68-69. — m INTRODUCTION IX F. M. Phillips, Journal of Educational Psychology, 191 6, had pupils of school grades of Fourth to Eighth work for ten minutes on arithmetic problems of addition, subtraction, multiplication and division. At the end of each minute the subject made a mark on the paper so that the experimenter knew what was done each minute by the subjects. In all the processes the best work was accomplished during the first minute. But the experimenter did not undertake to show whether there was fatigue or not. He found correlations between the first and last periods, in all the processes, ranging from .54 to .73, and says that the work of the first minute is less variable than that of later minutes, and that it is a fair index in all probability of one's ability in arithmetic. W. S. Painter, Journal of Educational Psychology, 1916, did mental multiplication of four-place numbers after much mental and physi- cal work which had resulted in a feeling of fatigue. He worked from 11 p. m. until 3:07 a. m. During the latter part of the experi- ment there was "a marked rise in time" per problem and the experi- menter thinks that "the outcome suggests strongly that there exists a definite and relatively abruptly appearing point beyond which mental work becomes impossible." While the time in per- forming the last three multiplications is high, the errors are rela- tively few. Mr. Painter believes, however, that after this abrupt point all mental work, properly so called, was practically impossible. __ CHAPTER I THE ADMINISTRATION OF THE EXPERIMENT The Subjects of the Experiment There were seven hundred and eleven subjects in these experi- ments. Three hundred and sixty-eight of them were children in the Third and Fourth grades, and three hundred and forty-three of them were children of the Seventh and Eighth grades of the public schools of Virginia, all white children. A large part of the number was from the city schools of Richmond and Petersburg. The smaller part was from the Training School of the State Normal School at Farmville, Va., and the public schools of Farmville, Va. The boys and girls were about equally divided and their ages were those of the average for the grades in which the tests were given. There was absolutely no selecting of subjects, but the experimenter took the cases where he could get them. For this reason it may be taken as a fact that the results represent the work of the average child of these grades. Materials Used The materials used were the Thorndike addition sheets, such as those used by Kirby in the experiment described in his "Practice in the Case of School Children," Teachers College, Columbia Uni- versity Contributions to Education, No. 53. There are seven differ- ent sheets. Each has forty-eight columns of one-place numbers, each column contains ten addends with the i's and the o's omitted, and each column is so arranged that any successive five of the columns are of a difficulty nearly, if not exactly, equal. These sheets were arranged in pads. For the Third and Fourth grades there were fourteen sheets, and for the Seventh and Eighth grade group there were twenty-one sheets in a pad. There was no possi- bility of a child's remembering the answers on a sheet which re- curred, because there would be no way of identifying that sheet. Eye strain was reduced to a minimum because the type is so very large, and besides, the eyes got a rest every two minutes. 2 MENTAL FATIGUE DURING CONTINUOUS EXERCISE Conditions of the Experiment Since the purpose of the experiment was to ascertain the be- havior of the child mind during a recitation, both the materials and the conditions of the experiment were made as nearly like a recitation — or a drill recitation — as was possible under the circum- stances. The materials were ordinary addition problems of one column, such as a teacher might use for a drill on adding and for improvement in number combinations. The experimenter gave all the tests in the presence of the regular teacher, and relied on his own teaching experience to put the child perfectly at his ease. There was nothing strained or strange about the experimenter's attitude but there was a constant endeavor to make the manner and atmosphere of the experiment entirely like that of an ordinary recitation-drill. The subjects were told that the experimenter wished to find out who was the best adder in the class and that papers would be passed for this purpose, if the class was agreeable to it. The stu- dents were usually eager to try. They were told that the papers would be examined and that the name of the best adder would be announced later on by the teacher. The pads were then passed to the pupils, face downward. The experimenter used a stop watch. At a signal the pupils turned the pads face upward and added for two minutes when time was called. As quickly as possible with no intentional intermission except such as was necessary to keep the class together, the class received the instruction to "take the next sheet" and the signal "go" was given, when they again worked two minutes by the stop watch. The intermissions were only about ten seconds long. But in this time the subjects raised their eyes to the experimenter who tried to maintain a 'sympathetic' counte- nance such as would keep them working happily. Nothing more was said to the class by the experimenter after the initial motiva- tion, excepting "take the next paper — get ready — go!" and after they had worked two minutes, "stop." The Third and Fourth grade pupils worked thus for twenty-eight minutes, and the Seventh and Eighth grade pupils for forty-two minutes. The pads supplied a record of what was done every two minutes by each pupil. After the total time had passed the pads were col- lected. Each pad bore the name, age, and school and grade of the pupil on the back written by the pupil when he received the pad. ADMINISTRATION OF THE EXPERIMENT 3 Method of Scoring With fourteen sheets to every one of the 368 Third and Fourth grade pupils and 21 sheets to every 343 Seventh and Eighth grade pupils, the experimenter secured 12,355 papers. For the Third and Fourth grades there were fourteen periods of two minutes each and for the older group there were twenty-one periods of two minutes each. When these papers were examined, a record was made of what each child attempted each two minutes, and another record of the accuracy of each child for every two-minute period. If a child attempted six columns, he received a credit for that two min- utes of six columns attempted. If only four of these were correct, he received credit on the accurate record sheet of only four columns. These two records, one of attempts and one of accurates, gave two tables, in the one case having fourteen columns 368 figures long, and in the other having twenty-one columns 343 figures long for at- tempts, and likewise the same for accurates. In short, we should say that the two groups of children — Third and Fourth grades and Seventh and Eighth grades — had two arrays of results, one for attempts and one for accurates. If a child's record showed itself incomplete — nothing attempted after a certain time — except in the last period or so, his work was not counted in the experiment. One child had to stop because of a slight illness which she had when she came to school that morning. Another boy was convalescent from typhoid fever and had to stop in the midst of the experiment. If a lack-a-daisical attitude toward the experiment was evidenced by any great omission of effort in the written record, the material was thrown out. But it so hap- pened that there was very little that had to be discarded. A child was given credit for what he did, both in quantity and quality. Time of Day and Year According to Heck's 1 experiments, the time of day makes little difference and so the experimenter made his tests at any time dur- ing the school day — early morning period, noon, and afternoon indiscriminately. Since there was a generous sampling of all times of the day, no one time of the day with its fatigue could assert itself 1 W. H. Heck, A Study of Mental Fatigue, 1913. 4 MENTAL FATIGUE DURING CONTINUOUS EXERCISE to any great extent. The test was intended to show what happens during a recitation at any time of the day. The time of the year was in the fall, in the winter, and in the spring. One class took its test when the snow was falling on the ground, a large part of the groups took their tests in November, and some of the classes worked with the windows open to the spring breeze. The tests were given during the time elapsing between December, 191 3, and November, 19 14. CHAPTER II ATTEMPTED AND ACCURATE PERFORMANCE The Group Curves Four curves are given herewith, plotted from the tables which accompany them. There are two work or attempts curves, one for Third and Fourth grades and one for Seventh and Eighth grades; and there are two accurates curves, respectively, for Third and Fourth grades and for Seventh and Eighth grades. In the Third and Fourth grade group there were 368 children participating and Periods FJcc" rehires .. a. -U U 4 5 6 7 8 9 10 11 Fig. I. Third and Fourth Grades 13 14 — 6 MENTAL FATIGUE DURING CONTINUOUS EXERCISE in the Seventh and Eighth grade group there were 343 who took part. The Third and Fourth grade group worked for twenty-eight minutes actually. This time was divided into fourteen periods of two minutes each. The horizontal line represents the time, in periods, during which the groups worked. The vertical line indi- cates the number of columns either attempted or accurately done. In the case of the work curve this vertical line indicates columns attempted whether right or wrong; in the case of the accuracy curve 7f U £> 3 2 X.-'^/ FJlUitpfs ffccurd-Jes j Li Periods 1 23 4 56 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Fig. 2. Seventh and Eighth Grades the vertical scale stands for columns correctly added. Every point on the curve was ascertained by finding the average attained by the group for that identical two-minute period of work. We shall call these the group curves. These curves are given here for the sake of presenting the facts derived by the experiment. These are mere gross results. The attempts and accuracy curves derived herewith do not afford a true idea of measurement of fatigue of the individuals during the work period of twenty-eight minutes for the Third and Fourth grade group nor for the forty-two minutes during which the Seventh and Eighth grade group worked. If instead of giving the average ATTEMPTED AND ACCURATE PERFORMANCE 7 we gave the quantity obtained by the group, this would emphasize the production by the group as a whole. These first curves give the changes in the group without regard to the changes of the individual. The curves following these will give the average of the individual curves and thus will regard individual changes. TABLE I Attempts of Third and Fourth Grades — Absolute Measures Columns attempted for each period of two minutes eriod Average A .D. P.E I 3. 15 1 .20 .058 2 3 35 1 17 .051 3 3 47 1 22 •053 4 3 48 1 34 • 059 5 3 27 1 17 .051 6 3 37 1 25 •055 7 3 45 1 34 • 059 8 3 54 1 33 .058 9 3 55 1 38 .061 10 3 57 1 39 .061 11 3 49 1 3i •057 12 3 28 1 3i ■057 13 3 5i 1 4i .062 H 3 38 I 36 .060 TABLE II Accurates of Third and Fourth Grades — Absolute Measures Columns accurate for each period of two minutes sriod Average A.D. P.E. 1 1 .70 1.27 .056 2 i-93 1 .1 .048 3 2. 11 1.32 .058 4 2.06 1.28 .056 5 1.88 1. 16 .051 6 2.07 1.24 •054 7 1.86 1 .21 • 053 8 1.99 1. 16 .051 9 1.98 1-34 ■059 10 1 .96 1.30 ■057 11 1.94 1 .27 .056 12 1.79 1.30 •057 13 1.82 1 .21 •053 14 1.78 1.30 •057 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE III Attempts of Seventh and Eighth Grades — Absolute Measures Columns attempted for each period of two minutes Period Average A D. P.E. I 6.02 I 67 ■075 2 5.62 I 39 .062 3 5-77 1 5 .068 4 5-92 1 61 .072 5 5 46 1 5i .068 6 5.78 1 55 .07 7 5-64 1 53 .069 8 5-8i 1 69 .076 9 5-68 1 77 .079 IO 5-98 1 52 .068 ii 5-94 1 56 .07 12 5.65 1 69 .076 13 5-99 1 5 .068 14 5-83 1 68 .076 15 6.23 1 95 .088 16 5-91 1 52 .068 17 6. 11 1 67 •075 18 5-95 1 84 .083 19 561 1 7 .077 20 6.02 1 78 .08 21 5-99 1 9i .086 TABLE IV Accurates of Seventh and Eighth Grades — Absolute Measures Columns accurate for each period of two minutes Period Average ^.P. P.E. 1 4.22 1.85 .083 2 4 04 1.63 .074 3 4 19 1.50 .068 4 4 30 1.83 .082 5 4 01 i-57 .061 6 4 18 1.94 .087 7 4 03 i-59 .072 8 4 22 1 .64 .074 9 4 64 1.65 .073 ATTEMPTED AND ACCURATE PERFORMANCE TABLE IV (Continued) Accurates of Seventh and Eighth Grades — Absolute Measures Columns accurate for each period of two minutes eriod Average A. D. P. E. 10 4-31 1.68 •075 ii 4.29 1. 71 .076 12 3-89 1.76 .079 13 4.19 i-74 .078 14 3-88 1 .76 .079 15 4.24 1. 91 .085 16 403 1. 71 .077 17 4.26 1 .72 .077 18 4.02 1 .72 .077 19 3-88 1.77 .080 20 3-93 1.83 .082 21 3-74 1.82 .081 Average of the Individual Curves The object in a study of this kind is to give every individual, whether his work is slow or fast, the same influence upon the final average. It is not fair to the poor or weak individual to put his small effort on a basis of absolute terms along with the effort of the better workers similarly expressed. The former may fatigue while the latter gain and a mean between them show essentially the curve of the better worker. The original data of the preceding tables fail to represent truly the facts which we wish to bring out because, as intimated above, the rapid workers with their larger measures of performance entirely swamp the changes that may occur in the work of the slower ones. But if everyone's work for the successive periods' is reduced to percentages of his total, the slow count the same as do the fast workers in determining the general work curve. For this reason we have derived percentage curves which represent more truly than the foregoing curves the central tendency of the whole group with regard to fatigue. With the absolute numbers we can examine the question of fatigue from the standpoint of one interested in the total product of a group, whereas by the personal curves we disregard the total products and examine changes in the 10 MENTAL FATIGUE DURING CONTINUOUS EXERCISE working ability of the individuals, and the general tendency of these individual changes. r -7 3 1 - T~h 1 yi 3| ?t4 h wftk Cfa 4^-s. $ccuv3{te.s J L i_J a / > J ¥■ s £ 7 ^ / /* // f>n t* ft y( u^ The curves shown herewith (Figures 3 and 4) are, however, only slightly different in form from the preceding curves. Every number in the distribution is a percentage of the total accomplished during the entire period of work for each installment of time for each child. A child did so much every two minutes for twenty-eight and forty- two minutes in the Third and Fourth grade group and the Seventh and Eighth grade group respectively. Percentages of these dis- ATTEMPTED AND ACCURATE PERFORMANCE II tributions were determined by dividing each two minutes' work by the total amount added during the whole period of work by each individual. This gave fourteen per cents, in the younger group for each child, and twenty-one per cents, in the Seventh and Eighth grade group for each child of that group. The fourteen average per cents, for the Third and Fourth grade group were obtained, —>efiA -zsriAciphtii trades. < 3 X v IV, Zf& o / x j *■ *r <£ 7 8 f >u (' /> '3 **■ T /<° '7 >* '/ -3-v «-/ 3j) J-o. Third and Fourth Grades H We next divide the curves into three parts, as nearly as possible thirds in the Third and Fourth group, and exact thirds in the Seventh and Eighth grade group. The former group is divided thus — four periods in the first part and five periods in the second and third parts. The fact that there were fourteen periods makes this unequal division necessary. The Seventh and Eighth grade group curve is divided into three parts, each containing seven ATTEMPTED AND ACCURATE PERFORMANCE 21 periods. In the accompanying table, No. IX, for Group Curves, if the reader will refer to VI, VII, and VIII, he will find the averages and ratios to which we are going to refer. In the case of the Third and Fourth grade group the average amount attempted each two minutes for this part of the curve (eight minutes) was 3.36 columns, for the second part or ten minutes following the first division of time, the average was 3.44 columns and for the last ten minutes of 6 r o 3 c/*J* J L J L J L Ft fr ~& - At t* npfs. highest tenth or upper tenth, as in the case of the Third and Fourth grades and the numbers were treated in the same way. These curves are handled in much the same way as the larger group curves. The idea here is to see if there is any difference in the form of a curve for a poor total accomplishment from that of the better accomplishment. INDIVIDUAL DIFFERENCES 33 T H NHfttfJfN ^H ^ &* * 1? ■8' ft 34 MENTAL FATIGUE DURING CONTINUOUS EXERCISE //t*.m X to w C */">** J /7cci4rat^ 0) Tn — i i i . i — i — r V » 4 **/ / / / / \ » / 1 / ^ / / / -/ < ( - H W 1 >\ i > >l > / >/ 6 ( > ) > / \ < * < ) v o v V>Yy'< > \ c < V»>> > - ) /< ?« \< - > ilk* ( I \ J / l\ ) \ 1 f ) ( I ri Co OQd (A I INDIVIDUAL DIFFERENCES 35 TABLE XII Attempts of Third and Fourth Grades The 368 cases are divided into ten groups on the basis of total amount done in twenty-eight minutes, going from lowest tenth to upper tenth. Below are given the averages for each First (Lowest) Tenth — 37 Cases 'erio d Average / .D. P.E 1 152 75 .11 2 1 5 63 .09 3 1 27 59 .08 4 1 19 59 .08 5 1 44 56 .08 6 1 36 67 .09 7 1 22 49 .07 8 1 33 60 .08 9 1 22 42 .06 10 1 36 61 .09 11 1 22 46 .06 12 1 33 5i .07 13 1 38 59 .07 H 1 08 39 •05 Third Tenth — k ?7 Cases erio d Average A .D. P.E. 1 2-43 7i . 1 2 2.29 64 .09 3 2-49 58 .08 4 2-37 54 .08 5 2.4 6 .09 6 2.52 49 .07 7 2.27 54 .07 8 2.4 56 .08 9 2-45 58 .08 10 2.29 53 .07 11 2-37 55 .07 12 2.02 47 .07 13 2.21 29 .04 14 2 08 6 .08 Second Tenth — 37 Cases Period Average / .D. P.E 1 1.84 55 .08 2 1.98 4i .06 3 1.98 3i •03 4 1.87 4i .06 5 1.76 5i .08 6 1.82 46 .06 7 2.0 27 . 1 8 1-9 42 .06 9 1.92 5 .07 10 2.05 45 .06 11 2.05 3 .04 12 1.85 46 .06 13 2.02 36 •05 14 2.08 6 .08 Fourth Tenth — 37 Cases Period Average / [.D. P.E 1 2-43 66 .09 2 2.92 55 .08 3 3.16 47 .07 4 2.84 6 .08 5 2.63 61 .09 6 2-79 54 .08 7 2-43 6 .08 8 2.76 47 .07 9 2.79 56 .08 10 2.9 47 .07 11 3.02 52 .08 12 2.71 79 . 11 13 2-73 54 .08 H 2.71 59 .08 36 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XII (Continued) Attempts of Third and Fourth Grades Fifth Tenth — 37 Cases Period Average /. .D. P.E 1 2-95 88 .12 2 3 4i 5 .07 3 3 29 45 .06 4 3 24 5i .07 5 3 05 46 .06 6 3 35 59 .08 7 3 37 •05 8 3 1 52 .07 9 3 05 46 .06 10 3 32 58 .08 11 3 13 51 .07 12 2 92 5 .07 13 3 21 54 .08 14 3 05 75 . 10 Seventh Tenth — 37 Cases Period Average A. D. P.E. I 3 37 76 .11 2 3 86 61 .09 3 3 92 40 .06 4 3 86 53 .07 5 3 57 62 .09 6 3 98 4i .06 7 3 92 62 .09 8 4 05 46 .06 9 4 18 5 .07 10 4 16 52 .07 11 4 05 46 .06 12 3 87 55 .08 13 4 02 47 .07 14 4 05 46 .06 Sixth Tenth — 37 Cases Period Average /. .D. P.E. 1 3-43 79 11 2 3 64 68 10 3 3 7 58 08 4 3 79 50 07 5 3 43 59 08 6 3 62 52 07 7 3 5i 58 08 8 3 57 6 08 9 3 64 56 08 10 3 37 65 09 11 3 45 68 10 12 3 27 55 08 13 3 76 61 09 14 3 32 76 10 Eighth Tenth — 37 Cases Period Average / . D. P. E. 1 4.29 85 12 2 4 02 69 10 3 4 34 64 09 4 4 29 64 09 5 4 16 56 08 6 4 40 63 09 7 4 13 67 10 8 4 56 79 11 9 4 64 75 10 10 4 29 79 11 11 4 32 61 09 12 3 94 67 093 13 4 16 64 089 14 4 34 93 132 INDIVIDUAL DIFFERENCES 37 TABLE XII (Continued) Attempts of Third and Fourth Grades Ninth Tenth— j 6 Cases Tenth Tenth — 36 Cases Period Average /. . Z). P. £. Period Average A.D. P.E I 4.21 85 .12 1 5.16 1 18 .17 2 4 61 71 .10 2 5.75 1 11 .16 3 4 58 79 -ii 3 6.05 1 13 -16 4 5 22 65 .09 4 6.25 1 13 .16 5 4 62 61 .09 5 5.78 1 22 .17 6 4 89 50 .07 6 5.39 1 09 -15 7 4 81 65 .09 7 6.61 1 57 -22 8 4 95 58 .08 8 6.58 1 47 -20 9 4 78 72 .10 9 6.92 1 60 .22 10 5 36 7 .10 10 6.75 1 56 .22 11 5 00 55 08 11 6.36 94 -13 12 4 64 73 .10 12 6.52 1 42 .20 13 4 78 67 .09 13 6.41 1 48 .20 14 4 44 78 .11 14 6.70 TABLE XIII 1 44 .20 Accurates of Third and Fourth Grades The 368 cases are divided into ten groups on the basis of total amount done in twenty-eight minutes, going from lowest tenth to upper tenth. Below are given the averages for each group First (Lowest) Tenth— 37 Cases erioO. Average /. .D. P.E 1 • 13 26 .04 2 •36 49 .06 3 .27 40 .06 4 .24 36 ■05 5 .29 43 .06 6 •32 43 .06 7 .21 34 •05 8 .16 27 .04 9 .40 56 .08 10 .21 34 •05 11 .21 34 •05 12 .21 33 •05 13 . .24 52 .08 H .18 3i .04 Second Tenth — 37 Cases zrio i Average / LD. P.E 1 •37 56 .08 2 81 77 .11 3 81 65 .09 4 5i 58 .08 5 67 58 .08 6 70 57 .08 7 78 59 .08 8 59 57 .08 9 48 52 .08 10 72 67 .09 11 40 54 .08 12 59 67 .09 13 62 60 .08 14 43 58 .08 38 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XIII (Continued) Accurates of Third and Fourth Grades Third Tenth — 37 Cases Period Average A. D. P.E. I 59 64 .08 2 1. 18 81 .11 3 1 13 58 .08 4 1. 00 7 .1 5 1.05 1 3 .18 6 •9i 59 .08 7 •75 65 .08 8 1.08 1 00 .14 9 •97 57 .08 10 .78 72 .10 11 .82 60 .08 12 .89 74 .10 13 .64 73 .10 14 .86 56 .08 Fifth Tenth — 3 7 Cases Period Average /. .D. P.E 1 1-55 74 .10 2 7i 78 .10 3 79 78 .10 4 79 77 .10 5 55 74 .10 6 87 76 .10 7 43 66 .09 8 60 74 .10 9 60 90 •13 10 45 79 .10 11 65 68 .09 12 18 63 .09 13 68 61 .09 14 49 85 •13 Fourth Tenth — 37 Cases Period Average A.D. P .E 1 1 .26 .82 11 2 1.40 .83 n 3 i-37 1.1 15 4 "•43 .66 09 5 113 •73 10 6 1.24 .65 09 7 1 .24 •7i 10 8 1-43 •74 10 9 1.05 •56 08 10 1. 18 .78 11 11 i-55 .76 11 12 .72 .76 1 1 13 1. 21 •79 11 H .90 .67 09 Sixth Tenth- —37 Cases Period Average A.D. P.E I 1 .90 1 .04 15 2 1-95 .88 12 3 2.18 •9i 12 4 2.00 .70 10 5 2.08 .64 09 6 2.29 .80 11 7 i-95 •77 11 8 1.87 1 .01 14 9 1.68 .80 1 1 10 2.02 •84 11 11 i-73 .98 U 12 1.63 ■71 10 13 i-73 •75 11 14 1.63 1.03 14 INDIVIDUAL DIFFERENCES 39 TABLE XIII {Continued) Accurates of Third and Fourth Grades Seventh Tenth — 37 Cases Period Average A.D. P.E i 1.89 .88 • 13 2 2.71 1 .00 •14 3 2-73 1.03 •14 4 2-73 .72 .10 5 1.79 .61 .09 6 2.52 .84 .11 7 2.10 .62 .09 8 2.21 .83 .11 9 2-44 .88 • 13 10 2.60 •79 .10 ii 2.27 .92 .12 12 2.08 •9i .12 13 2-35 .84 .11 H 2.16 .80 .11 Ninth Tenth — 36 Cases Period Average A.D. P.E. I 2 73 1 .04 15 2 3 57 .85 12 3 3 33 .88 12 4 3 63 .82 12 5 3 27 .82 12 6 3 10 • 73 10 7 3 13 •74 10 8 4 08 1.36 19 9 3 27 1.05 15 10 3 16 .86 12 11 3 45 •91 12 12 3 08 .82 12 13 3 40 •99 14 14 3 27 1 .01 15 Eighth Tenth — 37 Cases Period Average A.D. P.E 1 2.49 1 .04 15 2 2-79 1 .02 H 3 316 •74 10 4 2.98 •89 12 5 2-79 .86 12 6 3.00 .64 09 7 2.68 .88 12 8 2.82 1 .01 H 9 3.02 •79 10 10 2.84 1 .06 14 11 2-95 •72 10 12 2.29 .86 12 13 2-79 •97 H H 2.29 •74 10 Tenth Tenth- — 36 Cases Period Average A.D. P.E 1 3-84 .96 13 2 4 5 1. 16 16 3 4 78 1 .02 15 4 4 4i 1. 19 17 5 4 19 •93 12 6 4 67 1. 03 15 7 4 47 1 .02 15 8 4 73 .82 12 9 4 89 • 96 H 10 4 55 1.05 15 11 4 33 1. 14 16 12 4 25 1-34 19 13 4 08 1.36 19 H 4 30 1 .29 18 40 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XIV Attempts of Seventh and Eighth Grades The 343 cases are divided into ten groups on the basis of total amount done in forty-two minutes, going from lowest tenth to upper tenth. Below are given the averages for each group First (Lowest) Tenth— -35 Cases Period Average A l.D. P.E 1 3-71 1 13 16 2 3-42 89 13 3 3-37 65 09 4 3-66 87 12 5 3-17 68 10 6 3-55 73 11 7 3-17 61 09 8 3.08 63 09 9 3.20 56 08 10 3-40 57 08 11 3-15 57 08 12 2.83 64 09 13 3.22 55 08 14 309 68 10 15 2.87 64 09 16 3-25 70 10 17 3-31 77 11 18 306 70 10 19 3-57 98 14 20 3-57 84 12 21 2.86 65 09 Third Tenth — ^ ]4 Cases Period Average A l.D. I \E 1 4.88 76 09 2 4 74 62 12 3 4 83 68 11 4 4 68 57 12 5 3 88 53 11 6 4 68 57 07 7 4 21 69 11 8 4 77 68 09 9 4 7i 71 07 10 4 98 57 08 11 4 79 7i 10 12 4 38 56 08 13 5 00 52 10 Second Tenth — 35 Cases Perio d Average A.D. P.E 1 4-65 1 .24 ■19 2 4 85 .89 •13 3 4 00 ■74 .10 4 4 14 •63 .09 5 4 88 1 .02 .14 6 4 20 .60 .09 7 3 95 •50 .07 8 4 00 .80 .12 9 4 11 .61 .09 10 4 33 •58 .08 11 4 22 •73 .10 12 3 83 .48 .07 13 4 17 .80 . 12 14 3 8 .67 . 10 15 4 34 .84 . 12 16 4 3i •83 .11 17 4 58 ■72 .10 18 4 11 .82 . 12 19 3 75 .67 .10 20 4 3i •85 . 12 21 4 85 1.05 •15 Fourth Tenth — j 4 Cases Period Average A.D. P.E 1 4.89 1.03 ■14 2 4 86 •5i .07 3 4 94 .66 ■19 4 5 21 ■57 .08 5 4 74 •63 .09 6 5 11 ■73 .10 7 5 02 ■51 .07 8 4 94 .67 . 10 9 5 00 .70 . 10 10 5 06 •78 . 11 11 5 06 •50 .07 12 5 16 .80 .11 13 5 52 1 .09 ■15 INDIVIDUAL DIFFERENCES 41 TABLE XIV (Continued) Attempts of Seventh and Eighth Grades Third Tenth — 34 Cases Period .4 verage A.D. . P.E. 14 4-17 .63 .10 15 4 62 •75 .10 16 4 74 •49 .08 17 4 77 .76 .08 18 4 65 .86 .08 19 4 44 .72 . 10 20 4 83 .86 .09 21 3 59 .61 .11 Fifth Tenth- -34 Cases Period Average A.D. P.E 1 5-53 i-34 •19 2 5 09 .86 . 12 3 5 4i .69 .10 4 5 62 ■75 . 11 5 4 97 .86 .12 6 5 59 .67 .10 7 5 05 .72 .10 8 5 53 •73 .11 9 5 68 .62 .09 10 5 89 .86 .12 11 5 68 .83 . 12 12 5 45 .64 .09 13 5 7i •75 .11 14 5 38 .62 .09 15 6 29 1. 18 •17 16 5 74 .84 .12 17 5 7i .70 .10 18 5 45 .72 .10 19 4 42 1 .06 • 15 20 5 17 1 .04 •15 21 5 38 .81 . 12 Seventh Tenth — 34 Cases Period Average A.D. P.E 1 6.26 1. 00 •H 2 6. 17 •75 .11 3 6.32 .92 •13 4 6.26 .70 .10 5 5 74 .67 .10 Fourth Tenth — 34 Cases Period Average A.D. P.E. 14 5 17 80 12 15 5 26 85 12 16 5 29 86 12 17 5 21 67 19 18 4 12 1. 04 15 19 4 53 99 14 20 5 23 1. 11 16 21 4 86 69 10 Sixth Tenth — 35 Cases Period Average A D. P.E 1 5-98 1 29 19 2 5-75 62 09 3 5-89 73 11 4 5-8o 58 08 5 5-52 75 .11 6 5-92 63 .09 7 5-72 94 .14 8 5-92 84 .12 9 5-63 56 .08 10 6.08 85 .12 11 5-92 48 .07 12 5-89 56 .08 13 6.02 49 .07 14 6.20 68 .10 15 6.22 1 06 •15 16 5-78 68 . 10 17 5-92 74 .11 18 6.17 83 .12 19 5-8o 58 .08 20 6.36 90 • 13 21 6.22 74 .11 Eighth Tenth — < 4 Cases Period Average A .D. P.E 1 7.29 98 • 13 2 6.68 92 • 13 3 6.77 59 .08 4 6-95 72 . 10 5 6. *i 62 .09 42 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XIV (Continued) Attempts of Seventh and Eighth Grades Seventh Tenth — 34 Cases Period Average A D. T .E 6 6.38 86 12 7 6-33 74 11 8 6-35 84 12 9 5-92 52 07 10 6.23 81 12 11 6.32 77 11 12 6.00 76 II 13 6.48 88 13 14 6.98 97 14 15 7.23 1 14 16 16 6.44 87 13 17 6.58 93 13 18 6.41 72 10 19 5-68 86 12 20 6.26 1 19 17 21 6-35 1 02 15 Ninth Tenth— 3 4 Cases Period Average A D. I '. E 1 7-83 1 13 16 2 6 83 93 13 3 7 59 78 11 4 7 50 79 11 5 7 H 7i 10 6 7 29 59 08 7 7 41 83 12 8 7 76 92 13 9 7 26 69 10 10 7 65 82 12 11 7 74 78 11 12 7 25 78 11 13 7 62 79 11 H 7 45 88 13 15 8 27 1 48 21 16 7 02 62 09 17 6 77 79 11 18 7 28 1 05 15 19 7 29 1 01 14 20 7 92 65 09 21 8 14 1 25 18 Eighth Tenth — 34 Cases Period Average A. D. P. E. 6 6 62 .62 09 7 6-45 .65 09 8 7-05 .66 10 9 6.71 •59 08 10 6.80 .61 09 11 6.83 .61 09 12 6-59 .64 09 13 6.74 .62 09 14 6.38 •99 14 15 7-55 1 .00 14 16 6-95 •78 11 17 7.21 .89 13 18 6.69 .78 11 19 6.62 .70 10 20 7-05 .78 11 21 6.92 •98 14 Tenth Tenth- — 34 Cases Period Average A.D. P.E 1 9.29 1 .26 18 2 8 61 115 17 3 8 86 1. 18 17 4 9 44 i-3i 19 5 8 92 1-39 20 6 8 89 1 .09 16 7 8 98 115 17 8 8 95 1 .12 16 9 8 83 1 .04 15 10 9 38 1-25 18 11 9 27 1.30 19 12 9 52 1. 61 23 13 9 77 1 .60 23 14 9 95 1. 41 20 15 10 11 1 .60 23 16 9 68 i-73 25 17 9 98 1.50 22 18 10 44 2.18 3i 19 10 11 1.56 22 20 10 14 2.09 30 21 10 79 2-59 37 INDIVIDUAL DIFFERENCES 43 TABLE XV Accurates of Seventh and Eighth Grades The 343 cases are divided into ten groups on the basis of total amount done in forty-two minutes, going from lowest tenth to upper tenth. Below are given the averages for each group First {Lowest) Tenth — 35 Cases Second Tenth- —35 Cases Period Average A.D. F .E. Period Average A.D. 1 '. E. I i-43 1 .42 07 1 2.22 1 .00 14 2 86 1-37 06 2 2.37 .98 14 3 77 1. 19 05 3 2.20 1 .09 16 4 80 .96 04 4 2.40 1 .00 14 5 49 1 .01 05 5 2.55 .62 09 6 89 •98 04 6 2.49 •52 07 7 67 1.03 06 7 2.08 .96 13 8 52 .92 04 8 2.69 1.23 17 9 80 .88 04 9 2.40 •85 12 10 17 •85 04 10 2.75 •73 10 n 83 ■83 04 11 2.43 •93 13 12 02 .66 03 12 2.20 •77 11 13 54 1 .04 06 13 2.45 •94 13 14 45 •97 04 14 2.00 •85 12 15 40 •97 04 15 2.45 .92 13 16 58 .82 04 16 2.31 115 16 17 48 1 .04 06 17 2.28 1 .04 15 18 22 .84 04 18 2.34 1 .02 15 19 37 •95 04 19 2.02 •83 12 20 3i •93 04 20 2.05 .81 12 21 14 •7i 03 21 2.20 1.08 16 Third Tenth — 34 Cases Fourth Tenth — 34 Cases Period Average A.D. I '. E. Period Average A.D. 1 ». E 1 3 -32 1 .06 18 1 3-35 1 .10 16 2 2 95 .88 12 2 3 36 •78 11 3 3 26 .80 12 3 3 17 1 .10 16 4 3 4i .82 12 4 3 48 .82 12 5 3 08 •99 H 5 3 44 •79 10 6 3 05 1 .06 15 6 3 50 .82 12 7 3 00 •94 13 7 3 23 .84 12 8 2 89 1 .09 16 8 3 7i •92 13 9 2 74 •9i 13 9 3 23 .87 12 10 3 17 1.05 16 10 3 53 1.05 15 11 3 17 1 .09 16 11 3 68 ■94 13 12 2 54 1 13 16 12 3 17 •95 14 13 3 14 .88 13 13 3 75 1 .27 18 44 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XV (Continued) Accurates of Seventh and Eighth Grades Third Tenth — 34 Cases Period Average A.D. P.E. 14 2.69 1.08 16 15 2.74 .89 13 16 2.66 1.05 15 17 3.08 1 .06 15 18 2.83 •84 13 19 2.44 1 .02 15 20 2.71 •93 13 21 2-77 1 .02 15 Fifth Tenth- — 34 Cases Period Average A.D. 1 \E 1 4.09 1. 10 16 2 3-68 1 .20 15 3 3 56 •93 13 4 4-58 .78 11 5 3-59 .96 13 6 3-68 ■98 14 7 3-77 .90 13 8 365 .90 13 9 3-91 .78 11 10 3.80 •94 13 11 4.00 1. 11 16 12 3-40 1.08 15 13 3-50 •97 . 14 H 3.80 1. 19 17 15 3-86 1.06 15 16 3.62 •97 14 17 3-8o .80 12 18 3.65 1.23 18 19 3-ii .96 14 20 3-59 1. 41 ' 20 21 3.20 1. 41 20 Seventh Tenth — 34 Cases Perio d Average A.D. I \ E I 4.66 i-55 22 2 4-58 1 .29 19 3 4.89 1. 17 17 4 5-09 .96 13 5 5.06 .84 12 Fourth Tenth — 34 Cases Period Average A.D. P.E. 14 2 95 •95 14 15 3 38 1 .01 15 16 3 53 •99 14 17 3 59 •99 14 18 3 33 1 .09 15 19 3 11 .76 11 20 3 14 1.30 19 21 3 11 1. 18 16 Sixth Tenth- — 35 Cases Period Average A.D. P.E 1 3-98 1.49 21 2 4 44 1 . 11 16 3 4 17 1.03 15 4 3 89 1 .01 15 5 3 67 1.30 19 6 4 11 1. 14 16 7 4 26 1 .20 17 8 4 80 1 .12 16 9 4 36 •94 14 10 4 11 1 .20 17 11 4 62 •95 H 12 4 00 .68 10 13 4 50 1. 18 16 14 3 68 1 .10 16 15 4 23 1 .21 17 16 4 00 1. 14 16 17 4 H •93 13 18 4 26 1 .22 18 19 4 11 ■77 11 20 4 13 1 .01 15 21 4 12 1.30 19 Eighth Tenth — 34 Cases Period Average A.D. 1 '. E I 5-29 1 .12 17 2 4 92 .76 11 3 5 05 1 .12 16 4 5 44 1.05 15 5 4 83 1. 19 17 ■ UlM l WMMIim m »H* »MMWWW«MBq« BlinBSniHfMMH^HBnBfiSB^^HBragBBBBfl^aHHnBQEBHBIHBSBaOmaOB INDIVIDUAL DIFFERENCES TABLE XV {Continued) Accurates of Seventh and Eighth Grades 45 Seventh Tenth — 34 Cases Period Average A.D. P.E. 6 5 03 57 08 7 4 4i 1 04 15 8 4 77 63 09 9 4 48 1 00 14 10 4 38 1 25 17 11 4 76 1 31 19 12 4 23 1 02 15 13 4 83 1 07 15 14 4 29 1 24 17 15 4 74 1 20 17 16 4 29 1 08 16 17 4 74 1 02 15 18 4 86 1 04 15 19 4 26 1 28 17 20 4 11 1 08 16 21 4 00 1 29 18 Ninth Tenth- — 34 Cases Period Average A.D. I \ E I 5-95 i-37 19 2 5 45 1 .09 16 3 5 95 1 .00 14 4 5 92 ■77 11 5 5 59 1 .01 15 6 5 83 •98 13 7 5 86 .82 12 8 6 29 1 .01 15 9 5 92 •87 13 10 5 89 1 .06 15 11 5 95 1 . 12 16 12 6 08 •99 13 13 5 83 .98 13 H 5 80 1 . 11 16 15 5 24 1 .22 17 16 5 56 1. 16 17 17 6 23 ■87 13 18 5 98 1.09 16 19 5 83 •95 13 20 5 55 1.08 16 21 5 77 1 07 15 Eighth Tenth- — 34 Cases Period Average A.D. T .E 6 5-50 1.08 16 7 5 17 93 13 8 5 58 1 39 19 9 5 08 1 06 15 10 5 59 1 08 16 11 5 00 94 13 12 4 7i 1 12 16 13 5 20 90 13 14 4 95 1 12 16 15 5 35 1 4i 16 16 5 17 1 29 18 17 5 58 1 03 15 18 4 65 1 13 16 19 4 77 92 13 20 5 11 1 18 17 21 5 00 1 11 16 Tenth Tenth — 34 Cases Period Average A.D. P.E. I 7 59 1 43 .20 2 7 13 1 25 •17 3 7 23 1 5i .16 4 7 80 1 36 .20 5 7 14 1 08 .16 6 6 89 1 49 .20 7 7 08 1 03 •15 8 6 92 1 27 •17 9 6 98 1 15 .16 10 7 42 1 45 .20 11 8 02 1 33 .20 12 7 35 1 35 .20 13 7 95 1 54 .16 14 7 32 1 43 .20 15 8 32 1 66 .24 16 7 62 1 29 •17 17 7 38 1 74 ■25 18 7 32 1 83 .26 19 7 17 1 40 .20 20 7 17 1 20 .16 21 6 83 1 53 .16 46 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XVI Third and Fourth Grades. — Attempts Sub- Groups I II III IV V VI VII VIII IX 1 I 14 1-43 1.26 12% loss 1.37 1. 31 1.27 1. 00 ■95 .92 2 14 5 1.93 1.99 3% gain 1.92 1.88 2.01 1. 00 • 97 1 .04 3 6 12 2.40 2.10 12% loss 2.40 2.41 2.19 1. 00 1. 00 •91 4 3 1 2.84 2.72 4% loss 2.84 2.68 2.81 1. 00 and .94 7 -99 5 2 12 3.22 3.06 5% loss 3.22 3. 11 3.13 1. 00 .96 •97 6 4 12 3.59 3.45 4% loss 3.64 3.55 3.43 1. 00 .96 •94 7 9 1 3-72 3-98 7% gain 3-75 3-94 4«3 100 1.05 1 .07 8 8 12 4.22 4.16 1 % loss 424 4.40 4.22 1. 00 1.037 •99 9 10 1 4.47 4.62 3% gain 4.65 4.81 4.84 1. 00 1.034 1.04 10 9 1 5.65 6.54 16% gain 5.80 6.36 6.55 1. 00 1 .09 I 13 Third and Fourth Grades — Accurates Sub- Groups I II III IV V VI VII VIII IX 1 9 I .25 .21 16% loss .25 .28 .21 I. OO I. 12 .84 2 2 I .66 .55 17% loss .63 .64 .55 1. 00 3 1 00 .87 INDIVIDUAL DIFFERENCES 47 TABLE XVI (Continued) Third and Fourth Grades — Accurates Sub- Groups I II III IV V VI VII VIII IX 3 2 i .97 .80 18% loss .98 .95 .80 1. 00 .96 .81 4 11 12 1.34 .94 30% loss 1.36 1.22 1. 11 1. 00 .89 .81 5 6 12 1.68 1.45 14% loss 1. 71 1. 61 1.49 1. 00 •94 .87 6 6 14 2.01 1.66 17% loss 2.01 1.97 1.75 1. 00 •98 .87 7 3 5 2.44 2.20 10% IOSS 2.51 2.21 2.29 I. OO 4 .88 •91 8 3 12 2.81 2.46 12% loss 2.85 2.86 2.63 1. 00 1.003 .92 9 8 1 3.21 3.25 i%gain 3.32 3.37 3.27 1.00 1. 01 .98 10 9 1 4.37 4.21 4% loss 4.38 4.59 4.30 1.00 1.04 .98 TABLE XVII Seventh and Eighth Grades — Attempts Sub- Groups I II III IV V VI VII VIII IX 1 1 12 3.50 3.53 5% loss 3.44 3.14 3.21 1. 00 •9i •93 2 5 19 4-50 4-30 5% loss 4.38 4.07 4.32 1.00 •93 .98 3 13 21 4.82 4.29 11% loss 4.70 4.69 4.66 1. 00 •99 •99 4 13 18 4.90 4.87 i%loss 4.97 5.13 4.93 1. 00 1.03 •99 48 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XVII (Continued) Seventh and Eighth Grades — Attempts Sub- Groups I II III IV V VI VII VIII IX 5 15 19 5-34 4-99 7% loss 5.32 5.62 5.45 1.00 1.05 1.02 6 20 5 5.87 6.13 4% gain 5.80 5.95 6.07 1.00 1 .02 1 .04 7 15 19 6.25 6.10 2% loss 6.21 6.23 6.42 1. 00 I .00 1.03 8 15 14 6.91 6.86 i%loss 6.74 6.73 7.01 1. 00 ■99 1 .04 9 15 17 7.42 7.78 5% gain 7.37 7.53 7.53 1. 00 1.02 1 .02 10 21 2 8.92 10.35 16% gain 9.10 9.38 10.18 1.04 1.03 1. 12 Seventh and Eighth Grades — Accurates Sub- Groups I II III IV V VI VII VIII IX 1 10 12 1.69 1.27 25% loss 1.70 1.62 1.36 1. 00 •95 .80 2 10 14 2.26 2.09 8% loss 2.33 2.42 2.23 1. 00 1.08 •95 3 4 19 3.18 2.64 17% loss 3.15 2.91 2.75 1. 00 .92 .87 4 13 14 3.29 3.12 5% loss 3.36 3.43 3.31 1. 00 4 19 3-78 3-30 13% loss 3.85 3.23 3.55 1. 00 .84 .92 8 5 4.20 4.12 2% loss 4.07 4.29 4.14 1. 00 1.05 1. 01 4 21 4.7O 4-12 12% loss 4.82 4.63 4.42 1. 00 •93 •91 INDIVIDUAL DIFFERENCES 49 TABLE XVII {Continued) Seventh and Eighth Grades — Accurates Sub- Groups I II III IV V VI VII VIII IX 8 10 18 5.09 4.96 3% loss 5.17 5.16 5.09 1. 00 •99 .98 982 5.78 5.72 1 % loss 5-79 5-97 5-88 1.00 1.03 1. 01 10 15 21 7.32 7. 11 3%loss 7.27 7.42 7.42 1. 00 1 .02 1 .02 EXPLANATION OF TABLES NOS. XVI AND XVII In these tables we have under I. The maximum period for each curve. II. The minimum period for each curve. III. Average columns for first three periods. IV. Average columns for last three periods. V. Per cent, of gain or loss when III and IV are compared with III as a basis. VI. Average of first third of curve. VII. Average of second third of curve. VIII. Average of last third of curve. IX. Relative value of VI, VII, and VIII, using VI as a basis. The figures under V show that the group fatigued or did not fatigue — accord- ing as there was loss or gain. IX gives an idea of the general form of the curve. To begin with the facts as summarized in Table XVI. The location of the maximum (Column I) is certainly later with the better workers, when attempts are considered, in either the Third and Fourth or the Seventh and Eighth grades; the minimum, on the other hand, tends to come earlier with the better groups than with the poorer. In the case of accurates, no clear relation appears between the location of the maximum or minimum and the total accomplishment. Column V shows pretty clearly that the losses tend to be smaller towards the bottom of the column, which means that the better workers fatigued less than the poorer workers. In the case of attempts, the loss actually gives way to a gain, while in the case of accurates, the best workers lose very little at the end as compared with the beginning. Column IX, attentively considered, will show the same thing. 50 MENTAL FATIGUE DURING CONTINUOUS EXERCISE But, undoubtedly, the best presentation of the results is afforded by the curves. 1 The curves for attempts, in both the younger and the older group, show a clear general rise in the case of the upper tenth, indicating that the best workers increased their speed during the experiment; while the curve for the lowest tenth shows the c 4 a "o u I - C =4= =£= Periods 14 24 6 8 10 12 Fig. 9. Attempts — Third and Fourth Grades EXPLANATION OF FIGURES 9-12 The points on these curves are for the average performances for every four minutes, the data being handled thus so as to smooth out the curves. opposite course. The curves for the intervening tenths are rather confusing, but apparently have no definite tendency to deviate much from the horizontal — which would indicate that, on the whole, the medium workers neither increased nor decreased their speed. 1 See Figures 5, 6, 7, and 8 on pages 31, 32, 33 and 34 INDIVIDUAL DIFFERENCES 51 The curves for accurates fail to reveal to the eye any clear dif- ference between the sub-groups. Evidently we have made too many sub-groups in dividing into tenths. While highest and lowest tenths should evidently be kept separate, as their curves stand so definitely apart from the rest, the second and third tenths may very well be combined, and like- wise the eighth and ninth, leaving the four middle tenths to com- u C ft I III | i w*m I ty i Im i I. I inn ■ ■# Periods 2 4 6 8 10 12 14 Fig. 10. Accurates — Third and Fourth Grades bine into one central group. The resulting division into five unequal parts gives approximately equal spaces between the aver- ages of the adjacent groups, as should be the case according to the theory of distribution, and as appears in fact to be the case in the following curves constructed as above indicated. In order further to eliminate irrelevant fluctuations, the points on the curves indi- cate the averages of two adjacent periods of two minutes. The Tables, XVIII to XXI, give the averages for each period. Group A, in these tables, consists of the lowest tenth, Group B of the second 52 MENTAL FATIGUE DURING CONTINUOUS EXERCISE and third tenths, Group C of the fourth to seventh tenths, Group D of the eighth and ninth, and Group E of the uppermost tenth. ii I- a 6 5 -3? . i i i i \ I 1 I i i I t x j i i i ™4- Periods 24 6 8 10 12 14 16 18 20 21 Fig. 11. Attempts — Seventh and Eighth Grades The curves, thus reduced to their lowest terms, indicate pretty clearly that there is a relation in attempts between speed of work and liability to fatigue. The most rapid workers increase their speed as time goes by, while the slowest workers fall off, the middle groups remaining, on the average, almost perfectly steady for the time here considered. In accurate work, the general tendency of the whole group was shown in the last chapter to be slightly down- ward towards the end. But the decline comes later with the upper m INDIVIDUAL DIFFERENCES 53 group, and is somewhat less pronounced than in the lowermost group, at least when the decline is considered in relation to the height of the curve above the base line. This is brought out by another way of examining the results. 8 £ x ^ -^ ^»^ 7 6 D ^r*~ — ~ ^ x 03 B c 5 S 3 "3 U 4 C „^— ^^ 3 j5 ^^-- > '" 2 A I Periods 246 8 10 12 14 16 Fig. 12. Accurates — Seventh and Eighth Grades As heretofore, the first three periods were compared with the last three periods. The results are given below : Third and Fourth Grades Attempts Accurates Group A, 12 per cent, loss Group A, 16 per cent, loss Group B, 5 per cent, loss Group B, 18 per cent, loss Group C, 1 per cent, loss Group C, 18 per cent, loss Group D, 1 per cent, gain Group D, 6 per cent, loss Group E, 16 per cent, gain Group E, 4 per cent, loss Seventh and Eighth Grades Attempts Accurates Group A, 5 per cent, loss Group A, 25 per cent, loss Group B, 8 per cent, loss Group B, 12 per cent, loss Group C, 1 per cent, loss Group C, 8 per cent, loss Group D, 2 per cent, gain Group D, 2 per cent, loss Group E, 16 per cent, gain Group E, 3 per cent, loss 54 MENTAL FATIGUE DURING CONTINUOUS EXERCISE In the case of attempts, the relation between total speed and fatigue comes out in this tabulation as clearly as before. The loss shown by the slowest groups gives way to a gain with the quickest workers. In the case of accurates, the change is certainly less clear, and there is no passing over to a gain; yet it may fairly be said that the better groups show a smaller loss than the poorer. The facts of Column IX in Tables XVI and XVII are taken for the Groups A, B, C, D, and E of the previous tabulation. The facts for the lowest tenth are the facts for Group A, the second and third tenth are those for Group B, etc. Third and Fourth Grades A ttempts i 2 3 Accurates 1 2 3 Group Group A I .00 •95 .92 A 1. 00 1 . 12 84 B i .00 •985 •975 B 1 .00 .98 84 C 1 .00 •99 •99 C 1 .00 .92 87 D 1 .00 1-035 1. 015 D 1 .00 1 .01 95 E 1 .00 1 .09 1 13 E 1 .00 1.04 98 Seventh and Eighth Grades Attempts 1 2 3 Accurates 1 2 3 Group Group A 1 .00 • 91 •93 A 1 .00 ■95 80 B 1 .00 .96 •985 B 1 .00 1 .00 91 C 1 .00 1 .028 1 .02 C 1 .00 .96 955 D 1 .00 1.005 1.03 D 1. 00 1 .01 1 005 E 1 .00 1.03 1 . 12 E 1 .00 1 .02 1 02 In the case of attempts, the relation between total speed and liability to fatigue is about as clear in this present tabulation as it was in the previous one. The quickest workers gain and the poorest workers lose. In the case of accuracy the change is clearer, for in the younger classes the better workers show a smaller loss than the poorer ones and in the older classes the best workers show a small gain. Consequently this way of examining the results supports the conclusion that on the whole the slower work- ers fatigue more quickly than the more rapid workers. This, then, is put forward as one of the chief results of the experi- ment: that, on the whole, the slower workers fatigue more quickly than the more rapid workers. imiiiiiimiimn.iB.il INDIVIDUAL DIFFERENCES TABLE XVIII Attempts, Third and Fourth Grades 55 Group I Groups Groups I V, Groups Group . II, III V, VI, VII, VIII, IX A B C D E I 1-52 2.13 3-04 4-25 5-16 2 i 5o 2.13 3 46 4 31 5-75 3 i 27 2.23 3 52 4 4i 6.05 4 i 19 2. 12 3 43 4 75 6.25 5 i 44 2.08 3 17 4 39 5-78 6 i 36 2. 17 3 43 4 65 5-92 7 i 22 ' 2. 17 3 21 4 47 6.61 8 i 33 2.15 3 34 4 82 6.58 9 i 22 2.19 3 34 4 72 6.92 IO i 36 2. 17 3 44 4 82 6-75 ii i 22 2.21 3 66 4 66 6.36 12 i 33 195 3 19 4 29 6.52 13 i 38 2. 11 3 43 4 48 6.41 14 i 08 2. 12 3 28 4 39 6.70 TABLE XIX Accurates, Third and Fourth Grades Group I Groups Groups IV, Groups Group II, III V, VI, VII VIII, IX A B C D E I •13 •5i 1 65 2.61 3.84 2 •35 1 .00 1 94 3.18 4 50 3 .27 ■97 2 02 3-24 4 78 4 .24 76 1 99 3-30 4 41 5 •29 86 1 64 3-«3 4 19 6 •32 81 1 98 3-05 4 67 7 .21 77* 1 68 2.90 4 47 8 .16 86 1 78 3-45 4 73 9 .40 73 1 69 314 4 89 10 .21 77 1 81 3.00 4 55 11 .21 60 1 80 3.20 4 33 12 .21 74 1 40 2.68 4 25 13 •24 63 1 74 3 09 4 08 14 .18 65 1 55 2.78 4 30 56 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XX Attempts — Seventh and Eighth Grades Group I Groups Groups I V, Groups Group II, III V, VI, VII VIII, IX A B C D E I 3-7i 4-77 5.66 7 56 9.29 2 3-42 4 79 5 47 6-75 8 61 3 3-37 4 43 5 64 7.18 8 86 4 3-66 4 4i 5 72 7.22 9 44 5 3-17 4 38 5 24 6.77 8 93 6 3-55 4 44 5 75 7-45 8 89 7 3-17 4 08 5 63 6-93 8 98 8 3.08 4 39 5 68 7.40 8 95 9 3.20 4 4i 5 55 6.98 8 83 10 3 40 4 65 5 86 7.22 9 38 ii 3-15 4 50 5 74 7.28 9 77 12 2.83 4 11 5 60 6.92 9 52 13 3.22 4 59 5 93 7.18 9 77 14 3 09 3 99 5 93 6.92 9 95 15 2.87 4 48 6 25 7.91 10 1 1 16 3 25 4 52 5 81 6.98 9 68 17 3-31 4 68 5 85 6.94 9 98 18 3.06 4 38 5 54 703 10 44 19 3-57 4 09 5 11 6-95 10 11 20 3-57 4 57 5 73 7.48 10 14 21 2.86 4 22 5 70 7-53 10 79 INDIVIDUAL DIFFERENCES 57 TABLE XXI Accurates, Seventh and Eighth Grades Group I Groups Groups IV, Groups Group . II, III V, VI, VII VIII, IX A B C D E I i 43 2.72 4.02 5 62 7-59 2 I 86 2.66 4 01 5 19 7-13 3 i 77 2-73 3 89 5 50 7-23 4 i 8o 2.90 4 26 5 68 7.80 5 i 49 2.82 4 19 5 21 7.14 6 i 89 2.77 4 08 5 66 6.89 7 i 67 2-54 3 92 5 56 7.08 8 I 52 2.79 4 24 5 94 6.92 9 i 80 2-57 3 99 5 50 6.98 10 2 17 2.96 3 95 5 74 7.42 II I 83 2.80 4 26 5 47 8.02 12 I 02 2-37 3 70 5 39 7-35 13 I 54 2.79 4 14 5 52 7-95 14 I 45 2-34 3 68 5 37 7-32 15 i 40 2-59 4 05 5 79 8.32 16 i 58 2.48 3 85 5 36 7.62 17 i 48 2.68 4 07 5 90 7-38 18 I 22 2.58 4 02 5 32 7-32 19 i 37 2.23 3 65 5 30 7-32 20 I 3i 2.38 3 77 5 33 7.17 21 I 14 2.49 3 58 5 39 6.83 CHAPTER IV VARIABILITY OF THE INDIVIDUAL Dependence of Variability upon Central Tendency Everyone feels that variability is bound to increase as the mea- sure of performance increases. There is evidently some dependence of variability upon the absolute measure of performance, such that the greater the absolute measure of performance the greater the variability. Pearson has accepted the common-sense idea regarding this dependence, i.e., that variability is normally or typically propor- tional to the absolute measure of performance. Fullerton and Cattell, and Thorndike, following the rule governing the variable error in the theory of measurement, have held that the variability normally increases as the square root of the absolute measure of performance, though probably with modifications in different kinds of performance. Our data afford the opportunity of examining the variability of each individual from one period to another of the fourteen or twenty-one two-minute periods of the test, and then comparing the variability of individuals with smaller and greater total (or average) performance. This would be little to the purpose if a pronounced practice or fatigue effect occurred within the limits of the work; but, as these effects have been shown to be rather slight, the varia- bility that appears in the individual's performance can be accepted as, in the main, simply the ordinary variability of performance. UmMMNW *^ VARIABILITY OF THE INDIVIDUAL 59 TABLE XXII Accurates of Third and Fourth Grades, showing average performance and variability of each individual for the twenty-eight minutes "otal Average /. . D. C. T.ofA.D.'s .07 •13 .07 •13 .07 •13 07 • 13 07 13 ■13 2 14 25 2 14 25 2 14 25 2 14 25 2 14 25 ■25 3 21 34 3 21 34 3 21 34 3 21 34 3 21 34 •34 4 29 42 4 29 42 4 29 42 4 29 46 4 29 46 4 29 46 •44 5 36 73 5 36 73 5 36 66 5 36 66 5 36 66 5 36 66 5 36 66 .68 6 43 63 6 43 57 6 43 57 6 43 63 6 43 57 6 43 50 6 43 63 6 43 57 •58 7 50 64 7 50 61 7 50 61 6o MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXII (Continued) "otal Average A . D. C. T.ofA.D.'s 7 50 54 7 50 54 7 50 61 7 50 61 7 50 74 7 50 54 .60 8 57 60 8 57 52 8 57 67 8 57 60 8 57 60 8 57 60 .60 9 64 57 9 64 73 9 64 64 9 64 42 9 64 53 9 64 53 9 64 65 9 64 53 .58 IO 7i 52 IO 71 46 IO 7i 63 IO 71 75 IO 7i 82 IO 7i 75 IO 7i 75 IO 7i 68 IO 7i 72 IO 71 1 04 IO 7i 72 IO 7i 72 IO 71 81 •72 II •79 .67 II • 79 .69 II •79 •97 II •79 .81 II • 79 •9i .81 12 .86 .48 12 .86 •74 12 .86 •34 12 .86 .63 12 .86 •74 12 .86 .61 VARIABILITY OF THE INDIVIDUAL 61 TABLE XXII (C ontinn ed) Total .<4z>erage ^ .D. C. T.ofA.D. 's 12 .86 52 12 86 52 12 86 i 52 12 86 73 12 86 73 .69 13 93 80 13 93 53 13 93 68 13 93 70 13 93 80 13 93 70 13 93 57 13 93 68 13 93 52 13 93 I 05 13 93 70 .70 14 I oo 44 14 i 00 73 14 i oo 29 H i oo 73 14 i oo 58 H I 00 87 14 I 00 44 14 i oo 73 14 i oo 86 14 I 00 58 14 i oo 57 14 i oo 71 •63 15 i 07 92 15 i 07 63 15 I 07 34 15 i 07 53 15 i 07 53 15 i 07 66 15 i 07 73 15 i 07 66 15 i 07 63 15 i 07 63 15 i 07 80 .64 16 i 14 62 16 I 14 64 16 i 14 60 16 i 14 75 •65 17 i 21 56 •56 62 MENTAL FATIGUE DURING CONTINUOUS EXERCISE Total TABLE XXII {Continued) Average A.D. C. T. of A. D.'s. 18 I 29 8 1 18 I 29 61 18 I 29 72 18 i 29 64 18 I 29 61 18 I 29 75 18 i 29 94 19 1 36 73 19 1 36 57 19 I 36 69 19 1 36 98 19 1 36 1 II 19 1 36 73 19 1 36 54 19 1 36 74 19 I 36 ■S3 19 1 36 78 20 1 43 64 20 1 43 69 20 1 43 72 20 1 43 77 20 1 43 63 20 1 43 63 20 1 43 7-' 20 1 43 63 21 1 50 86 21 1 50 7i 21 1 50 57 21 1 50 50 21 1 50 1 00 21 1 50 78 21 1 50 64 22 1 57 55 22 1 57 55 22 1 57 83 22 1 57 57 22 1 57 91 22 1 57 57 22 1 57 97 23 1 64 82 23 1 64 69 23 1 64 1 21 23 1 64 59 23 1 64 44 .72 ■77 .68 .72 .70 II ■ VARIABILITY OF THE INDIVIDUAL TABLE XXII (Continued) 63 Total Average A.D. C. T.ofA.D.'s 23 1 64 82 23 1 64 1.08 .80 24 1 7i •75 24 1 7i •75 24 1 7i •75 24 1 7i •75 24 1 7i 1 .02 24 1 7i .72 24 1 7i •65 24 1 7i •55 24 1 71 .89 24 1 71 1 .02 24 1 7i •75 24 1 7i .90 •79 25 1 79 1.09 25 1 79 .72 25 1 79 1.07 25 . 1 79 1 .09 25 ' 1 79 1.50 25 1 79 .72 25 1 79 •72 25 r 79 •93 25 1 79 •44 .92 26 1 86 • 87 26 1 86 ■63 26 1 86 .87 26 1 86 .89 26 1 86 1.28 26 1 86 .87 26 1 86 .87 26 1 86 1 .00 •9i 27 1 93 .66 27 1 93 •93 27 1 93 .66 27 1 93 ■95 27 1 93 .66 ■77 28 2 00 .84 28 2 00 ■58 28 2 00 .70 28 2 00 .70 28 2 00 .70 28 2 00 1.06 28 2 00 .70 j»9 2 07 •93 64 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXII (Continued) Total Average A.D. C. T.ofA.D.'s. 29 2.07 .66 29 2.07 1.08 29 2.07 • 79 29 2.07 .66 .82 30 2.14 .86 30 2.14 .62 30 2.14 .98 30 2.14 .86 30 2. 14 .62 30 2.14 .86 .80 31 2.21 .80 3i 2.21 •73 31 2.21 .84 3i 2.21 1 .04 3i 2.21 •95 3i 2.21 ■49 .81 32 2.28 1.03 32 2.28 •59 32 2.28 •93 32 2.28 •50 32 2.28 •75 32 2.28 1.23 .84 33 2.36 1. 16 33 2.36 • 78 33 2.36 .68 33 2.36 .78 33 2.36 •83 33 2.36 .68 33 2.36 •78 • 33 2.36 .83 33 2.36 .68 33 2.36 •87 33 2.36 •78 33 2.36 .68 .80 34 2-43 1.04 34 2-43 •85 34 2-43 •78 34 2-43 .90 .89 35 2.50 •93 35 2.50 •85 35 2.50 1 13 35 2.50 •63 35 2.50 1. 00 35 2.50 1.05 •94 MMHUMI VARIABILITY OF THE INDIVIDUAL 65 TABLE XXII {Continued) Total Average A.D. C. T.ofA.D.'s 36 2.58 .70 36 2.58 .90 36 2.58 1. 19 36 2.58 1.29 36 2.58 .70 •95 37 2.64 1.24 37 2.64 1 .06 37 2.64 1. 16 37 2.64 .69 37 2.64 .98 37 2.64 1. 00 37 2.64 .82 .96 37 2.64 .69 38 2.71 .76 38 2.71 i-43 38 2.71 1. 17 38 2.71 •95 38 2.71 •79 1.02 39 2-79 .70 39 2.79 •73 39 2.79 •84 39 2-79 .81 39 2-79 1.26 .87 40 2.86 .60 40 2.86 .92 40 2.86 •74 40 2.86 •78 .76 4i 2-93 .82 41 2-93 .64 41 2-93 •94 41 2-93 1.20 41 2-93 •94 •91 42 300 1 .20 42 3.00 •94 42 3.00 •57 42 3.00 .66 42 3.00 •54 42 3.00 .66 42 3.00 .81 42 3.00 1.08 ■73 43 307 1. 14 43 3 07 .92 43 307 ■77 43 307 .80 66 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXII {Continued) Total Average A .D. C. T.ofA.D.'s 43 3-07 52 43 3 07 37 •75 44 3 14 66 44 3 14 1 16 44 3 14 1 16 •99 45 3 21 83 45 3 21 1 06 45 3 21 93 45 3 21 1 09 .98 46 3 28 98 46 3 28 79 46 3 28 89 46 3 28 98 4.6 3 28 89 •9i 47 3 36 9i 47 3 36 74 47 3 36 81 47 3 36 1 01 47 3 36 91 47 3 36 67 .84 48 3 43 1 20 48 3 43 93 48 3 43 99 48 3 43 1 13 48 3 43 99 48 3 43 1 13 48 3 43 99 1.05 49 3 50 63 49 3 50 84 49 3 50 77 49 3 50 84 ■77 50 3 57 7i ■71 51 3 64 76 51 3 64 61 5i 3 64 .80 .72 52 3 71 1 04 52 3 7i 74 .89 54 3 86 1 00 54 3 86 1 15 54 3 86 73 .96 55 3 93 1 06 55 3 93 79 55 3 93 94 55 3 93 94 •94 yvihiiiiuiiuiih VARIABILITY OF THE INDIVIDUAL 67 TABLE XXII {Continued) Total Average A.D. C. T.ofA.D.'s 56 4.00 •56 •56 57 4 07 •77 57 4 07 •77 •77 58 4 14 •75 58 4 14 1. 41 58 4 H 1. 16 1. n 59 4 21 •93 59 4 21 1. 18 1.06 60 4 28 •47 60 4 28 .68 •57 61 4 36 1 .09 1 .09 62 4 43 I-5I 62 4 43 1 .02 1 .26 64 4 57 .96 64 4 57 .96 .96 65 4 64 •74 •74 66 4 7i 1 .04 1.04 68 4 86 •87 •87 70 5 00 .70 .70 7i 5 07 .66 .66 72 5 14 .87 .87 73 5 21 •83 •83 76 5 43 1.03 1.03 85 6 07 1 .21 1 .21 no 7 85 I .02 1.02 TABLE XXIII Showing the Data for Third and Fourth Grades, Accurates with C. T.'s and Average A. D.'s Combined into Twelve Groups C. T. A .D .07 to .43 40 50 to 86 67 93 to 1 29 65 1 36 to 1 7i 75 I 79 to 2 14 13 2 21 to 2 58 87 2 67 to 3 00 88 3 07 to 3 43 92 3 50 to 3 86 81 3 93 to 4 28 84 4 36 to 5 21 90 5 43 to 7 85 1 09 The twelve groups given here were obtained by combining the data of Table XXII so that as nearly as possible the twelve groups would proceed by steps of .36. The data would not submit to this treatment in the last two groups of the twelve. 68 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXIV Attempts, Third and Fourth Grades, Showing Average Performance and Average Variability of Certain Groups of Individuals for the Twenty-eight Minutes. Eighty-five Groups Number of Columns Number of Columns Number of Columns C. T. Average C. T. Average C. T. Average of A.D. of A.D. of A.D. .28 55 2.36 62 4.07 49 •43 49 2-43 52 4 14 81 .64 55 2.50 67 4 21 60 .78 34 2-57 53 4 28 70 .86 24 2.64 4i 4 35 79 1. 00 10 2.71 67 4 43 67 1.07 13 2.78 54 4 50 68 1. 14 29 2.86 59 4 57 62 1. 21 46 2-93 4i 4 64 71 1.28 4i 3.00 42 4 7i 89 1-35 60 307 68 4 78 1 18 1-43 56 3-14 53 4 85 55 1.50 58 3.21 49 4 93 42 i-57 57 3-28 67 5 00 33 1.64 47 3-35 55 5 07 95 1. 71 58 3-43 66 5 14 1 08 1.78 54 3-50 66 5 21 42 1.83 47 3-57 64 5 28 60 i-93 37 364 56 5 36 62 2.00 46 3-71 71 5 43 65 2.07 37 3-78 60 5 50 64 2.21 55 3-92 49 5 64 53 2.28 56 4.00 23 5 5 5 6 6 6 6 6 6 7 7 8 9 13 78 85 93 00 07 28 43 50 2 93 00 43 7i 79 < 6 4 ; 58 51 82 57 67 79 72 H 53 43 92 78 J.21 5.72 wmaoomimiMiiimii VARIABILITY OF THE INDIVIDUAL 69 TABLE XXV Showing Data for the Foregoing Table Combined into Twelve Groups Average of A. D. .46 •45 •58 •51 ■59 63 ■55 73 69 67 81 4i In this table we proceed as nearly by steps of .36 as possible. The first group and last four groups could not well be made to fulfill this condition. But as this does not affect the mathematical significance of the results, it matters little. C. T .28 to 1. 71 I 78 to 2. 14 2 25 to 2-57 2 64 to 3.00 3 07 to 3-43 3 50 to 3-86 3 92 to 4.28 4 35 to 4-71 4 78 to 5-28 5 36 to 5 -7o 5 78 to 6-93 7 00 to 13.64 TABLE XXVI Accuracy, Seventh and Eighth Grades, Showing Average Performance and Average Variability of Certain Groups of Individuals for the Forty-two Minutes of Working. There are 122 Groups Number of Columns Number of Columns Number of Columns c '. T. Am '.rage C. T. Average C T. Average ofA.D. ofA.D. ofA.D. •43 53 2.38 1 . 10 3-57 1.05 48 59 2-43 1 .21 3 62 1 00 62 65 2.48 1.07 3 67 90 7i 82 2.52 •83 3 7i 1 24 76 58 2-57 1.30 3 76 1 08 90 61 2.62 1 .01 3 81 1 15 1 04 93 2.67 1.04 3 86 1 23 1 29 92 2.71 ■99 3 90 65 1 33 51 2.76 .82 3 95 1 11 1 38 89 2.81 1.05 4 00 1 19 1 43 1 37 2.86 .84 4 05 1 00 1 62 99 2.90 .90 4 10 1 09 1 81 77 2-95 .60 4 14 1 09 1 86 1 62 3.00 .76 4 19 98 1 90 1 03 3-05 1. 00 4 24 1 27 1 95 73 3 09 ■97 70 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXVI (Continued) Number of Columns Number of Columns Number of Columns C. T. Average C. T. Average C. T. Average ofA.D. ofA.D. of A .D. 3-14 1.02 4.29 1 38 2.00 .48 3 19 • 7i 4 38 1 07 2.05 .78 3 24 •97 4 43 1 12 2.O9 ■92 3 29 1 .04 4 48 90 2. 14 .89 3 33 .83 4 52 1 21 2. 19 •95 3 38 1 .11 4 57 1 08 2.24 .83 3 43 1 .09 4 62 1 15 2.29 115 3 48 •89 4 67 1 11 2-33 1 .01 3 52 1. 21 4 71 1 49 4.76 1. 16 5 33 1 .02 6 09 1 03 4.81 1 . 11 5 43 1. 81 6 14 1 39 4.86 1.84 5 48 1 .26 6 19 99 4.9O 1. 61 5 52 1 .46 6 28 1 08 4-95 •97 5 57 i-54 6 43 1 30 5.00 .67 5 62 1. 10 6 48 1 22 505 1 .24 5 7i 1 .01 6 57 95 509 1. 14 5 76 1. 14 6 62 1 14 5- H 1. 14 5 86 .86 6 76 1 32 519 1. 16 5 90 .87 6 90 1 28 5-24 i-34 5 95 .46 6 95 1 17 529 .98 6 00 .86 7 05 78 7 14 1 44 7 19 1 38 7 48 1 4i 7 57 1 3i 7 67 1 85 7 71 1 35 7 80 1 35 8 00 1 33 8 14 1 04 8 52 98 8 71 1 59 9 33 1 49 11 52 1 65 Mi VARIABILITY OF THE INDIVIDUAL TABLE XXVII 71 Showing Data of Foregoing Table Con ibined into Twelve Groups Average C. T. ofA.D. ■ 43 to 1.90 •85 1.95 to 2.38 .88 2.43 to 2.86 1 .02 2.90 to 3.33 .88 3.38 to 3.81 1 .07 3 . 86 to 4.29 1 .10 4.38 to 4.76 1. 14 4.81 to 5.24 115 5.29to 5.71 1.28 5.76 to 6.19 •95 6.28 to 6.62 1. 14 6 . 76 to 1 1 . 52 1-34 The data of Table XXVI could not be easily handled in a graphic representa- tion, consequently it was combined into twelve groups as in Table XXIII. In this particular table we proceed as nearly by steps of .43 of a column as possible. The first and last groups of the series could not be well made to go by the step. TABLE XXVIII Showing Central Tendencies and Corresponding Average A. D. of Columns Attempted by Groups of Individuals of Seventh and Eighth Grades. There are 127 Groups Number of Columns Number of Columns Number of Columns C. T. Average C. T. Average C. T. Average ofA.D. of A.D. ofA.D. 2. 14 .70 5- 2 9 •65 8.00 2.22 2.43 68 5 33 62 8 05 1 13 2.76 58 5 38 94 8 09 79 2.81 61 5 43 79 8 14 4i 2.90 61 5 48 1 04 8 24 67 2-95 1 17 5 52 77 8 62 1 13 3.00 29 5 57 82 8 7i 74 305 54 5 62 73 8 81 92 309 53 5 67 65 8 86 1 12 3-19 1 15 5 7i 92 9 09 88 3 24 67 5 76 1 05 9 29 64 329 62 5 81 57 9 33 1 27 3-33 5i 5 86 81 9 38 93 3-38 69 5 90 79 9 52 1 02 3-43 53 5 93 66 9 57 88 72 MENTAL FATIGUE DURING CONTINUOUS EXERCISE Number of Columns TABLE XXVIII {Continued) Number of Columns Number of Columns c 7\ Average C. T. A verage C. T. Average ofA.D. ofA.D. ofA.D. 3-52 69 6.00 72 9.67 92 3 57 •79 6.05 83 9.71 84 3 67 64 6.09 64 10.24 1 03 3 7i 90 6. 14 75 10.57 89 3 76 1 20 6.19 72 10.62 9i 3 81 62 6.24 1 H 10.71 99 3 90 88 6.29 9i 10.76 89 3 95 1 14 6-33 1 24 11 . 19 81 4 00 76 6.38 81 1 1 • 43 1 29 4 05 76 6.43 83 1 1 . 62 2 77 4 09 67 6.52 83 11.86 5 H 4 H 92 6-57 69 13-09 1 63 4 19 65 6.62 95 4 24 65 6.67 70 4 29 72 6.71 72 4 33 68 6.76 65 4 38 72 6.86 61 4 43 20 6.90 63 4 48 51 6-95 7i 4 52 1 10 7-05 89 4 57 59 7.09 98 4 62 69 7.14 30 4 67 74 7.19 61 4 7i 57 7.24 56 4 76 55 7.29 92 4 81 99 7-33 96 4 86 68 7-38 64 4 90 45 7-43 90 4 95 78 7.48 1 69 5 00 38 7-52 71 5 05 70 7-57 68 5 09 68 7.62 87 5 19 74 7.71 97 5 24 1 26 7.76 88 7.82 83 7-95 88 The data of Table XXVIII could not be readily handled graphically, and were consequently combined into twelve groups as in Table XXV. In this particular table we proceed as nearly by steps of .7 of a column as possible, but it is difficult to do this because at the beginning and ending of the series — and in the middle — the numbers were so very much scattered. The best grouping was made that could be made. This does not impair the mathematical value of the graph. VARIABILITY OF THE INDIVIDUAL 73 TABLE XXIX Showing Data of Foregoing Table, Combined into Twelve Groups C. T. 2 . 14 tO 2.90 2.95 to 405 4 . 09 to 4.76 4.81 to 5-48 5.48 to 6.19 6 . 24 to 6.90 6.95 to 7.62 7.71 to 8.24 8 . 62 to 8.81 8.86 to 9.71 10.24 to 10.76 1 1. 19 to 13.09 Average of A.D. 64 75 66 76 77 82 81 98 93 94 94 34 The actual facts for the present test are seen on comparing the average variability with the absolute measure of performance. (See the accompanying tables — XXII-XXVIII — which give, for the indi- viduals having the same central tendency, the average of their A. D.'s.) Each of these tables is followed by a regrouping which brings out more fully the tendency of the A. D.'s to increase with the C. T. In the absence of any universally accepted law, we can take these figures (Tables XXII, XXIV, XXVI, XXVIII) as our basis and see what law of dependence would fit them best. We have assumed Var. that this law would have the form r T a = C. and find what value of the unknown n will give best agreement with this law. That is, we are to find such a root of the C. T. as will give the most constant quotient when divided into the corresponding variability. Thus two methods were used for determining what value of n gave the closest approximation to a constant ratio: 1. Find for what value of n the variability of the quotient is least. 2. Observe for what value of n the curve approaches most closely to the horizontal line. 74 MENTAL FATIGUE DURING CONTINUOUS EXERCISE Tables XXX, XXXI, XXXII, XXXIII give the Average, Aver- x age Deviation, and Probable Error for each value of — in attempts ya and accurate performance. TABLE XXX Showing for Accurates of Third and Fourth Grades the Central Tendency and x Average Deviation of Different Values of — , where x = A. D., y=C. T. yn Values of X y Values of X yih Values of X y\ Values of X Values of X y—* Values of X y-h Values of X y\ Values of X y\ Values of X y\ Values of X y\ Values of X yis Values of X Average .489 A. D. .302 P. E. •254 Average •549 A. D. . 1227 P. E. . 104 Average ■559 A. D. .119 P. E. . 100 Average •569 A. D. .1065 P. E. .090 Average ■577 A. D. . 1011 P. E. .085 Average •593 A. D. . 10069 P. E. .084 Average .613 A. D. .088 P. E. •075 Average .646 A. D. .090 P. E. .076 Average .691 A. D. .096 P. E. .081 Average .7089 A. D. .108 P. E. .091 Average .7283 A. D. .111 P. E. .094 Average •793 AD. .150 P. E. .127 VARIABILITY OF THE INDIVIDUAL 75 TABLE XXXI Showing for Attempts of Third and Fourth Grades the Central Tendency x and Average Deviation of Different Values of — Average .241 A. D. .130 P. E. .012 Average .376 A. D. .126 P. E. .011 Average .453 A. D. .130 P. E. .011 Average .501 A. D. .167 P. E. .016 Average .560 A. D. .192 P. E. .016 Average .596 A. D. .212 P. E. .019 Average .615 A. D. .225 P. E. .017 Average .700 A. D. .290 P. E. .026 TABLE XXXII Showing for Accurates of Seventh and Eighth Grades the Central Tendency x and Average Deviation of Different Values of — Average .329 A. D. .1431 P. E. .011 Average .558 A. D. .1133 P. E. .009 Average .684 A. D. .1057 P. E. .008 Average .766 A. D. .1196 P. E. .091 Average 1.069 A. D. .2079 P. E. .054 Values of X y Values of X y\ Values of X y\ Values of X yi Values of X yi Values of X Values of X y ia Values of X Values of X y Values of X Values of X Values of X yi Values of X 76 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXXIII Showing for Attempts of Seventh and Eighth Grades the Central Tendency x and Average Deviation of Different Values of — -Vn Values of X y Values of X yh Values of X y\ Values of X yi Values of X Average .148 A. D. .048 P. E. .004 Average •346 A. D. .085 P. E. .006 Average .467 A. D. .107 P. E. .008 Average •542 A. D. .116 P. E. .009 Average .86 A. D. •304 P. E. .0228 Explanation Tables XXXIV, XXXV, XXXVI, and XXXVII give the different values of x — combined into twelve groups. (See Figures 13, 14, 15, and 16.) X Figures 13 to 16 show graphically the position of each value of — on a vertical y a scale for increasing total performance on a horizontal scale. Total TABLE XXXIV Accuracy, Third and Fourth Grades, Values ys Average Average Average Average Average Average Average y o 19 y* yrr* y—> ym 1 to 6 .40 1.67 82 79 74 .69 72 7 to 12 .67 ■ 99 82 85 80 .81 78 13 to 18 .65 • 59 62 62 62 • 63 61 19 to 24 •75 .48 60 60 62 .63 64 25 to 30 •83 .42 59 59 61 .62 64 31 to 36 .87 36 55 56 59 .60 62 37 to 42 .88 • 31 5i 52 55 • 56 60 43 to 48 .92 .28 49 5i 53 • 55 57 49 to 54 .81 .21 34 42 45 .46 49 55 to 60 .84 .20 40 4i 44 .46 48 61 to 73 .90 • 19 40 4i 44 .46 48 76 to no 1 .09 .16 41 43 47 • 49 52 VARIABILITY OF THE INDIVIDUAL 77 Total TABLE XXXIV {Continued) Average Average Average Average Average y* yx yt ys y~o I to 6 62 67 50 47 46 7 to 12 76 74 71 70 69 13 to 18 63 64 64 64 64 19 to 24 65 67 70 71 72 25 to 30 66 70 74 75 78 31 to 36 65 70 76 78 80 37 to 42 62 66 74 77 79 43 to 48 62 69 75 79 81 49 to 54 53 59 64 69 71 55 to 60 51 59 66 65 72 61 to 73 54 61 69 74 77 76 to no 59 69 79 86 90 TABLE XXXV Attempts, Third and Fourth Grades, Values Total A ver- Aver- Aver- A ver- A ver- A ver- A ver- A ver Number of age age %ge age age age age age Columns X X X X X X X X y yh y% y\ y\ y\ yiz 4 to 24 46 54 48 46 46 46 46 46 25 to 30 45 28 32 38 38 40 41 42 31 to 36 58 36 43 46 49 49 49 53 37 to 42 5i 18 30 35 39 42 45 46 43 to 48 59 18 33 36 4i 48 5i 53 49 to 54 63 17 32 41 45 49 54 55 55 to 60 55 13 27 35 39 44 48 48 61 to 66 73 17 32 46 49 56 60 63 67 to 74 69 H 3i 40 46 52 57 59 75 to 80 67 12 28 39 44 50 54 57 81 to 97 81 13 32 44 51 60 62 57 98 to 191 2 4i 23 54 1 11 1 34 1 63 1 78 1 9i 78 MENTAL FATIGUE DURING CONTINUOUS EXERCISE TABLE XXXVI Accuracy, Seventh and Eighth Grades, Values of V" Total Average Average Average Average Avi vrag Columns X X X X X y y\ yi y~\ 9-40 .85 81 80 .82 *3 41-50 .88 41 60 67 75 51-60 1 .02 39 63 74 80 61-70 .88 21 52 60 64 71-80 1 .07 30 58 68 79 81-90 1 . 10 27 54 69 77 91-100 1. 14 25 53 69 78 IOI-IIO 115 23 52 67 77 III-I20 1.28 23 55 73 86 I2I-I30 •95 17 35 52 61 I3I-I40 1. 14 18 45 61 7i I4I-242 i-34 17 48 67 80 TABLE XXXVII x Attempts, Seventh and Eighth Grades, Values of — Total Average Average Average Average Average Columns X X X X X y yi yi yi 45-6i 64 249 •397 464 502 62-85 75 215 •403 495 542 86-100 66 153 .296 405 458 101-115 76 148 •335 429 507 111-130 77 131 .316 424 524 I3I-I45 82 126 •329 441 515 146-160 84 143 .301 415 495 162-173 98 122 •346 488 581 181-185 93 107 •315 452 507 186-214 94 IOI .312 451 542 215-221 94 089 .289 437 527 226-275 2 34 196 .672 1 on 1 254 ■■ m VARIABILITY OF THE INDIVIDUAL ■Mt/e/npfe 3n) an* 4M Grades - ~ ]/a/aes ft ' y Y % X V *-■*■ + + IS h* hi /.* u f J .7 ..(, ,6' .9 .3 .V ] ./ 4-34 25-30 31-36 37-4Z 43-48 49-5* 55-60 61-66 6T-T4- , 75"-8o~8/-9y 98-191 TOTAL.. COLUMNS Corrected Variability in Attempts Figures 13 and 14 give the graphical representation for the attempts data of corrected variability for the younger and older groups respectively. 80 MENTAL FATIGUE DURING CONTINUOUS EXERCISE Attempts Ttf.and 8tt.Graetesy*fa/ ues tr>£l t I .* ,7 y j "X. ^ •» -*T ■§" *— H «t VARIABILITY OF THE INDIVIDUAL 8l For the Third and Fourth grades attempts, Figure 13 shows the — 1, — and — r lines to be nearly horizontal, but the preference goes y? yi y-i X to the —j value as it is the most nearly horizontal line of those lines y? I \f //tcurafeS -Jretrfr/i.fcnJcs ji V^/ut "7TE 7-/1. 13-1* /f-ifts-J p-JL w Wt* *f-W jp& y-73 -jiftij Total Columns and besides the —, series has the smallest average deviation of all yi ° X the different series of the — values. yn As to the attempts data of corrected variability for the Seventh and Eighth grades, the - values and the -7 values compete most y y? 82 MENTAL FATIGUE DURING CONTINUOUS EXERCISE flccur&Jes- K- 8"'6rc?c/es ft Values 1-tf 13 (•' f.o ■1 % •7 ♦6 if $ v I { y* _x X yi _X y &£./£ ***** * & A s^ ,-. r \ V-. /\\ / — .,. AW / w a> >\ / --•' V \ V- .--*■ V / o 9_^ 4 ,-5 5/. eo 6 |_yo 71-80 61-90 9l-ioo /oi-ito 111-120 121-130 Ql-i4-oi«i»24Z strongly for the preference. We have chosen here, however, the - line, since it appears to be the most nearly horizontal one and the y judgment seems justified by the fact that the average deviatioh of HUB VARIABILITY OF THE INDIVIDUAL 83 the - series is smaller than that of the other series. But the experi- y menter thinks that the cause of this inconsistency is due to the fact that some of the subjects at the last attempted too recklessly and thus impaired the data to a small extent. If this had not hap- pened the y* value would have been, the writer believes, the chosen value of y k . (Figure 14.) n - * " JTc cur* /eS - 7***1** ■- jrtUtftr - F, ■f'7 Figure 17 gives the different positions on a vertical scale for the A. D. of each x — series for both groups in both attempts and accurates. In the case of the . . X Third and Fourth grades, in attempts, the curve drops lowest for the -7 series; ■v 2 x but in accurates it is lowest in the — series of values. In the case of the Seventh . x and Eighth grades, in attempts, the curve is lowest in the - series; but in the x accurates it goes lowest in —1 as it did in the accurates for the younger children. 3/3 84 MENTAL FATIGUE DURING CONTINUOUS EXERCISE Corrected Variability in Accurate Performance For corrected variability in accurate performance of Third and Fourth grades, Figure 15 shows the lines for values of—, — and — -y? ys yf X (when these are taken respectively as in the expression — ) to be yn all of them nearly horizontal with the preference for a value between y* and y* values. We have taken, however, the line representing the y 11 value as the one most nearly horizontal of those in the figure. Also this value has the smallest average deviation from the average. And since these two criteria are those which shall decide in the case, Var. ,~ „,i = C. is the formula taken here. (C. T.y What has been said of the Third and Fourth grades group may also be said of the Seventh and Eighth grades group, Figure 16. While the — , — and — lines are all nearly horizontal, the line y? yn yi representing the y 3 values is probably the one most nearly hori- zontal; and since the y* series of values has the smallest average x deviation, we give the preference to this value of — and so Var. . y* , _ „ .1 = C. is the formula taken here for this data. However, it (c. T.y is possible here as above that a value lying somewhere between y* and y* is the correct one for the data of accurate performance. I think these results agree for the total work and for the accurate x work. Total work gives greatest constancy at — for Third and yi Fourth grades and - for Seventh and Eighth grades. Accurate y work, in the handling of these data gives, or very close to, — in both y* the younger and older groups. It is likely that the data do not lend themselves in their handling to bearing out the theoretical facts. x Theoretically this should be — . yi ■■»■!■■ VARIABILITY OF THE INDIVIDUAL 85 Variability and Performance Var. Var. Now, if we accept the formula in one case r T \ = C, or _ _ i = C, as fitting the general run of our facts, having based our correction upon the general run of our own data, of course we cannot find whether those who do less or do more are more variable since what we have done shows them equally variable. But we can from this graph of the accepted law of dependencies see if there are any eccentricities not according to the normal. We may say that the group has variability in excess of the general run of the data, or that it is close to the general run of the data. In all the graphs illustrating the accepted law of dependencies we find the last one or two ratios departing, or so tending, from the norm and likewise the first one or two. In the case of the accurate performances for the younger group, this departure from the norm is only slight (see Figure 15 — y" line). With the older group the departure at beginning and end is a little more pronounced (Figure 16). But in the case of the attempts data the departure is quite pronounced, especially at the end of the -r and - lines, for both groups. We may then say that this shows a tendency for the subjects who attempt most, and also for those who attempt least, to exceed the normal variability to some extent. This surplus of variability in the slowest and quickest workers is probably due to the fact that they show, more than the medium workers, a progressive change throughout the course of the work, the quickest workers increasing their speed as the work proceeds, and the slowest workers gradually slackening (See pp. 49-54). -M VITA THOMAS RUSSELL GARTH Born at Paducah, Kentucky, December 24, 1872. Entered Union City Public High School, 1891. Completed High School course at Warren Academy, Denver, Colorado, and diploma granted 1905. Four years of High School work. Entered University of Denver, September, 1905. Graduated from same June, 1909, with A.B. degree. Post-graduate work at University of Denver for one year, 1909-1910. Degree of Master of Arts granted in June, 1910. Graduate student in Columbia University, 1912-1913, 1915-1916. V t~i f Deacidified using the Bookkeeper process. Neutralizing agent: Magnesium Oxide Treatment Date: Nov. 2004 PreservationTechnologies A WORLD LEADER IN PAPER PRESERVATION 1 1 1 Thomson Park Drive Cranberry Township, PA 16066 (724) 779-21 1 1 LIBRARY OF CONGRESS HI! III! II II 1 1 II III III II II 013 228 035 6